help guttmanl

Title

guttmanl -- Guttman lower bound reliability coefficients

Syntax

Reliability coefficients for data

guttmanl varlist
[if] [in] [weight]
[, options ]

Reliability coefficients from covariance or correlation matrix

guttmanl matname
[, sds(matname2) ]

where varlist is

[(]varlist[)]
[ [||]
[(]varlist[)] ]

parentheses around varlist denote reversed
sign while || indicates split-halves

matname is a covariance (or correlation) matrix

aweights and fweights are allowed; see weight.

Description

guttmanl computes lower bound reliability coefficients
as proposed by Guttman (1945).

There are different ways to estimate the split-half reliability
(lambda 4). As noted by Guttman (1945), any split will qualify
as a lower bound to reliability. guttmanl considers all
((2^n)/2 - 1) possible splits to find the maximal lambda 4. This
is computationally intensive and might not be feasible with a
large number of items. The || notation may be used to
estimate lambda 4 for one specific split instead.

guttmanl optionally applies the method proposed by Hunt
and Bentler (2015) to estimate the split-half reliability. The
authors suggest to use a random series of locally optimal lambda
4 coefficients and then draw quantiles of interest from the
resulting empirical distribution. This approach is feasible
with a large number of items and provides less upwardly biased
estimates in small samples.

Type guttmanl to replay previous results.

Options

lambda(numlist [, not]) requests
Guttman's lambda numlist (not) be estimated. By default
all six coefficients are computed. The option may also be used
to replay coefficients.

quantiles[([numlist]
[, quantiles_options])]
estimates the numlist quantiles of lambda 4 from a series of
locally optimal split-halves (cf. Hunt and Bentler 2015). If not
specified, numlist defaults to 0.05 0.5 0.95. The
quantiles_options are

reps(#) specifies the number of repetitions, i.e. the
number of random split-halves. Default is 1,000.

rseed(#) sets the random-number seed. See set seed.

asis specifies that the sign (direction) of variables
(items) be taken as is. Enclosing one or more variable names
in varlist in parentheses implies asis. If not
specified, the sign of variables is determined using
factormat.

casewise|pairwise|em are mutually exclusive
and specify the treatment of missing values.

casewise is
the default and specifies only complete cases be used for
calculations. cw is a synonym for casewise.

pairwise requests pairwise calculation of
covariances. pw is a synonym for pairwise.

em obtains covariances from the EM algorithm used by
mi impute mvn. This approach is suggested for estimating
reliability coefficients by Izquierdo and Pedrero (2014) and for
factor analysis by Truxillo (2005). Specify em(em_options)
to control the EM process.

min(#) is used with pairwise or em to further
restrict the sample. It includes only cases with at least #
non-missing values in varlist. Default is min(1),
meaning all available cases are used.

std performs calculations based on standardized
(mean 0, variance 1) variables (items).

sds(matname2) is used with a correlation matrix as
input. It may neither be specified with a covariance matrix
nor with a varlist.

Example

. webuse automiss

. guttmanl price headroom rep78 trunk weight length turn displ

. guttmanl price headroom rep78 trunk weight length turn displ , pw std

Saved results

guttmanl saves the following in r()

Scalars

r(lambda#) Guttman's lambda #

r(k) Number of items in the scale

r(N) Number of observations
(not with pairwise)

r(reps) Number of repetitions
(quantiles only)

Macros

r(cmd) guttmanl

r(varlist) variable names (unique)

r(signlist) sign of variables

r(halves) split-half indicators for maximal lambda 4

r(wtype) weight type

r(wexp) weight expression

Matrices

r(L4Q) lambda 4 quantiles (quantiles only)

r(C) covariance matrix

r(N) pairwise number of observations
(pairwise only)

References

Benton, T. (2015). An empirical assessment of Guttman's
Lambda 4 reliability coefficient. In: Millsap, R. E.,
Bolt, D. M., van der Ark, L.A., Wang, W-C. (Eds.)
Quantitative Psychology Research. The 78th Annual Meeting of the Psychometric
Society. Springer: Cham Heidelberg New York Dordrecht London. pp.301–310.

Guttman, L. (1945). A BASIS FOR ANALYZING TEST-RETEST
RELIABILITY. Psychometrika, 10(4), 255-282.

Hunt, T. (2013). Lambda4: Collection of Internal Consistency
Reliability Coefficients. R package version 3.0.
http://CRAN.R-project.org/package=Lambda4

Hunt, T.D., Bentler, P.M. (2015). Quantile Lower Bounds to
Population Reliability Based on Locally Optimal Splits
Reliability Coefficients. Psychometrika, 80(1), 182-195.

Izquierdo, M.C., Pedrero, E.F. (2014). Estimating the
reliability coefficient of tests in presence of missing
values. Psicothema, 26(4), 516-523.

Truxillo, C. 2005. Maximum likelihood parameter estimation
with incomplete data. Proceedings of the Thirtieth Annual
SAS(r) Users Group International Conference.
(pdf)

Acknowledgments

The code used to find lambda 4 borrows from the R package
Lambda4 (Hunt, 2013) and code provided by Benton (2015).

Some of the details in the code are borrowed from Joseph Coveney's
glambda2
(posted on Statalist).

A request from Paul van Kessel on
Statalist
stimulated this program.

Author

Daniel Klein, University of Kassel, klein.daniel.81@gmail.com

Also see

Online: alpha

if installed: guttmanl()